Tension in a string tied between a wall and a lamp suspended from the ceiling

• thoughtclaw
In summary, the small restaurant needs to move a table in order to have space for a new lamp, and attaches a second string to the lamp and runs it horizontally to the wall. The tension in the string is due to the force of the second string and gravity.

Homework Statement

The owner of a small restaurant needs to move a table in order to have space for a new display. Ordinarily, a lamp of mass m is hanging over the table, suspended from a string attached to the ceiling. With the table in a new position, the lamp needs to be moved. To this end, the owner attaches a second string to the lamp and runs the string horizontally to the wall. (a) Draw a free body diagram. (b) Derive an expression for the tension in the horizontal string. Your answer should be in terms of m, g, and the angle (theta).

(Sigma)F=ma

The Attempt at a Solution

I've gotten as far as Ft+Fg=ma, but I'm not at all confident in that equation, and I feel a lot of trepidation in attempting to go forward from here.

How many forces act on the lamp? Where's your diagram? (If you can't attach one, at least describe it.)

Hint for b: Consider horizontal and vertical components.

I believe the only forces acting on the string are the tension from the wall and the force of gravity. The diagram shows the string coming from the ceiling and the lamp, with the other string coming from the wall to the right, and an angle (theta) going between the first string and the x axis. I have the x-axis going straight left-to-right and the y-axis going straight from up and down.

thoughtclaw said:
I believe the only forces acting on the string are the tension from the wall and the force of gravity.
You want the forces acting on the lamp, not on the string. The wall's not in contact with the lamp, so it cannot exert a force on it.

It's the strings that exert tension on the lamp!
The diagram shows the string coming from the ceiling and the lamp, with the other string coming from the wall to the right, and an angle (theta) going between the first string and the x axis. I have the x-axis going straight left-to-right and the y-axis going straight from up and down.
Good. So where do the forces act?

So it's the tension from the second string, and the force of gravity. Right? The tension from the second string is acting toward the wall, and the force of gravity is of course toward the floor.

By the way, thanks very much for your help!

thoughtclaw said:
So it's the tension from the second string, and the force of gravity. Right?
Don't forget the first string! In what direction does its force act?
The tension from the second string is acting toward the wall, and the force of gravity is of course toward the floor.
Good.

I guess I was of the impression that the tension in the first string was negligible and could be ignored, but I obviously shouldn't make that assumption. Its force of tension is toward the spot in the ceiling it's hung from.

Thanks again!

thoughtclaw said:
I guess I was of the impression that the tension in the first string was negligible and could be ignored, but I obviously shouldn't make that assumption.
If its tension were negligible, then you could cut that string and nothing much would happen. Do you think that's the case?
Its force of tension is toward the spot in the ceiling it's hung from.
Right. Better include it in your diagram!

Excellent point! How could I have overlooked that?

I'm still not sure how to derive the expression for this right off, but I'll work on it. Thanks again, Doc Al!